{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:C4AYH7Q6RV5D4YXU322XEC7IGH","short_pith_number":"pith:C4AYH7Q6","schema_version":"1.0","canonical_sha256":"170183fe1e8d7a3e62f4deb5720be831fd69d4456833b6876b8ab4f7b909263d","source":{"kind":"arxiv","id":"math/0510358","version":1},"attestation_state":"computed","paper":{"title":"A Beurling theorem for noncommutative L^p","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"David P. Blecher, Louis E. Labuschagne","submitted_at":"2005-10-17T19:07:55Z","abstract_excerpt":"We extend Beurling's invariant subspace theorem, by characterizing subspaces $K$ of the noncommutative $L^p$ spaces which are invariant with respect to Arveson's maximal subdiagonal algebras, sometimes known as noncommutative $H^\\infty$. It is significant that a certain subspace, and a certain quotient, of $K$ are $L^p({\\mathcal D})$-modules in the recent sense of Junge and Sherman, and therefore have a nice decomposition into cyclic submodules. We also give general inner-outer factorization formulae for elements in the noncommutative $L^p$. These facts generalize the classical ones, and shoul"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0510358","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2005-10-17T19:07:55Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"10626c009a3fd9f0f3cc449aba8a9789d35ed4a693944e8fff305b50400967a1","abstract_canon_sha256":"3184528e84150f96dc79cf9fa01268e2789eb8f161713781d8318edaa34ed62f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:51:12.746347Z","signature_b64":"5QFNnyxuxe9ri99biVBQ9AxKLCCjCXk9c0U338RRUBYAGnIAxuhyN0L5zeH5WZj/g9Iifs6DGAvoIyDGNKAXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"170183fe1e8d7a3e62f4deb5720be831fd69d4456833b6876b8ab4f7b909263d","last_reissued_at":"2026-07-04T14:51:12.745957Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:51:12.745957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Beurling theorem for noncommutative L^p","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"David P. Blecher, Louis E. Labuschagne","submitted_at":"2005-10-17T19:07:55Z","abstract_excerpt":"We extend Beurling's invariant subspace theorem, by characterizing subspaces $K$ of the noncommutative $L^p$ spaces which are invariant with respect to Arveson's maximal subdiagonal algebras, sometimes known as noncommutative $H^\\infty$. It is significant that a certain subspace, and a certain quotient, of $K$ are $L^p({\\mathcal D})$-modules in the recent sense of Junge and Sherman, and therefore have a nice decomposition into cyclic submodules. We also give general inner-outer factorization formulae for elements in the noncommutative $L^p$. These facts generalize the classical ones, and shoul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510358","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0510358/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0510358","created_at":"2026-07-04T14:51:12.746018+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0510358v1","created_at":"2026-07-04T14:51:12.746018+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510358","created_at":"2026-07-04T14:51:12.746018+00:00"},{"alias_kind":"pith_short_12","alias_value":"C4AYH7Q6RV5D","created_at":"2026-07-04T14:51:12.746018+00:00"},{"alias_kind":"pith_short_16","alias_value":"C4AYH7Q6RV5D4YXU","created_at":"2026-07-04T14:51:12.746018+00:00"},{"alias_kind":"pith_short_8","alias_value":"C4AYH7Q6","created_at":"2026-07-04T14:51:12.746018+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C4AYH7Q6RV5D4YXU322XEC7IGH","json":"https://pith.science/pith/C4AYH7Q6RV5D4YXU322XEC7IGH.json","graph_json":"https://pith.science/api/pith-number/C4AYH7Q6RV5D4YXU322XEC7IGH/graph.json","events_json":"https://pith.science/api/pith-number/C4AYH7Q6RV5D4YXU322XEC7IGH/events.json","paper":"https://pith.science/paper/C4AYH7Q6"},"agent_actions":{"view_html":"https://pith.science/pith/C4AYH7Q6RV5D4YXU322XEC7IGH","download_json":"https://pith.science/pith/C4AYH7Q6RV5D4YXU322XEC7IGH.json","view_paper":"https://pith.science/paper/C4AYH7Q6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0510358&json=true","fetch_graph":"https://pith.science/api/pith-number/C4AYH7Q6RV5D4YXU322XEC7IGH/graph.json","fetch_events":"https://pith.science/api/pith-number/C4AYH7Q6RV5D4YXU322XEC7IGH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C4AYH7Q6RV5D4YXU322XEC7IGH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C4AYH7Q6RV5D4YXU322XEC7IGH/action/storage_attestation","attest_author":"https://pith.science/pith/C4AYH7Q6RV5D4YXU322XEC7IGH/action/author_attestation","sign_citation":"https://pith.science/pith/C4AYH7Q6RV5D4YXU322XEC7IGH/action/citation_signature","submit_replication":"https://pith.science/pith/C4AYH7Q6RV5D4YXU322XEC7IGH/action/replication_record"}},"created_at":"2026-07-04T14:51:12.746018+00:00","updated_at":"2026-07-04T14:51:12.746018+00:00"}